In the oil industry, electromagnetic (EM) induction surveys are used to map the electrical conductivity of geologic formations between boreholes and/or radially away from a single wellbore. The latter, usually referred to as induction logging, has been in routine use for over fifty years. Those surveys are performed in open holes; that is, holes that have not been lined with a (typically, metal) casing.
Recently, the concepts of induction logging have been extended to surveys between uncased wells and between wells cased with conductive liners. There is also interest in the use of logging between surface and downhole sensors, and within single wells that are cased with conductive liners. The conductive liners (casing) introduce several problems. For example, the signal from the transmitter to the receiver is severely attenuated upon passing through the conductive casing because of the casing's high conductivity and, usually, high magnetic permeability (high-mu or high-μ). The conductivity, permeability, and thickness of the casing wall can vary along the length of the casing. Transmitters in these surveys are normally multi-turn solenoids that have a core of high magnetic permeability. At high current levels in the solenoid, the permeability of the core material, and of the surrounding casing itself, is driven into a nonlinear regime. Under those circumstances, the current in the solenoid is not proportional to the net radiated field. (Receivers may also use high-mu, cored solenoids, but because they never operate at the high field levels in which such nonlinear effects are seen, this is not a problem for them, in practice.)
The various types of induction surveys typically share many commonalities. A transmitter, usually a multi-turn coil of wire, carries an alternating current of frequency co (radians/sec). This creates a time-varying magnetic field in the surrounding formation that in turn, by Faraday's law, induces an electromotive force (emf). This emf drives currents in the formation that are basically proportional to the formation conductivity. Finally, a receiver is positioned either in the same hole as the transmitter, in another hole, or on the surface, and measures the magnetic field arising from the transmitter and the secondary, or induced, currents in the formation. Conventional induction logging always uses a combination of multiple receivers and/or multiple transmitters connected in series so as to cancel the mutual signal in air. In general, a theoretical model for a logging system embedded in a formation of arbitrary resistivity is used to match or interpret the received signals. In some applications, the absolute value of the average formation resistivity is not as important as the ability to map variations of resistivity within the formation. To determine this spatial variation of formation resistivity, the surveys typically involve placing the transmitter at multiple locations in the hole and measuring the fields at multiple receiver locations for each transmitter location. In crosshole surveys, this yields a data set similar to those obtained from tomography.
There is a “window” of frequencies in which such surveys are practical. Below a certain frequency, the secondary fields from the formation are simply too small to be detected with practical receivers. Above a certain frequency, the casing attenuation obliterates the formation response. The frequency window depends greatly on the type of casing used. Carbon steel casing generally has a conductivity (σ) of approximately five million S/m and a relative permeability (μr) of approximately 100. Chromium casing is essentially non-magnetic (μr is equal to or close to 1), and has a conductivity of approximately one million S/m. As a result, chromium casing is preferable because it attenuates the EM signal much less than the carbon steel casing, at the same frequency. Thus, for practical field systems in chromium cased boreholes, this window can be up to several hundred Hz, while in carbon steel cased boreholes, the frequency is limited to roughly up to one hundred Hz.
Recall, however, that even in those frequency windows, the casing properties (i.e., conductivity (σ), relative permeability (μr), thickness (t), and inner/outer diameter) are not constant along the length of casing. Since the casing attenuation is so strong, small variations in the casing's properties produce variations in the fields seen by a receiver that are large compared to the variations expected from desired formation variations. A further problem is that the strength of the transmitter, known as its moment, must be known so that moment variations are not misinterpreted as variations in the formation conductivity.
There are prior attempts to eliminate, or correct for, those casing variations. Removing the casing effects from the measurements provides huge benefits on the image quality of an EM inversion/imaging. Consider the schematic for a crosswell survey (FIG. 1). The transmitter Ti produces a field Bij at receiver Rj, which is the product of:Bij=MigijKfijkjki=GijKfijkjki  (1)The factors above include the moment (or strength), Mi, of transmitter Ti, and a purely geometric term, gij. Those two factors are combined to produce Gij. The desired formation response, that is, the response from the induced currents if no casing were present, is represented by Kfij. The casing attenuation at the transmitter is represented by ki, and the casing attenuation at the receiver is represented by kj. It has been shown that the casing attenuation terms ki and kj are in fact multiplicative for simple (ideally point) transmitters and receivers operating in homogeneous casing.
One attempted solution to the casing problem is to use ratios of received fields to eliminate ki and kj. As an illustrative example of this method, suppose the receiver borehole is not cased, so that kj is one. For a fixed position of the transmitter, one can take the ratio of fields at two different receiver positions A & B:[Bij(A)/Bij(B)]=[Gij(A)Krij(A)ki]/[Gij(B)Kfij(B)ki]  (2)Under those conditions, the casing attenuation ki cancels out. The Gijs are known, so the full ratio yields a formation response ratio that is casing independent. Such response ratios can be fitted to models of the formation just as easily as the responses themselves. This method can easily be extended to double ratios if both boreholes are cased.
This method, however, has two principal problems: (1) the ratios are very sensitive to noise in the measured fields; and (2) in the modeling or inversion process, the use of ratio data reduces the sensitivity to variations in formation resistivity near the boreholes (e.g., near the transmitter borehole in the above example).
An alternative solution to the ratio approach described above can reduce the effects of noise by inverting the casing attenuation factors and formation property simultaneously. However, such an approach also reduces the sensitivity to variation in formation resistivity near the boreholes, which reduces the resolution of the resistivity/conductivity image obtained from the EM inversion/imaging. Imposing appropriate constraints on the casing attenuation factors can enhance the inversion.
Another solution, at least for the cross-borehole mode of operation, is to place an auxiliary receiver adjacent to the transmitter (or auxiliary transmitter adjacent to the receiver). Consider FIG. 2 for the case in which it is desired to find the casing correction for the transmitter when the receiver Rj is in an open-hole. The field at the auxiliary receiver Bik is:Bik=Gikkikk  (3)because the spacing between the transmitter and auxiliary receiver is too small for there to be any formation response. The field at the distant receiver is:Bij=GijKfijki  (4)
If the auxiliary receiver Rk is sufficiently far from the transmitter Ti, if Rk and Ti have the same coupling to the casing (i.e., same length of solenoid, same core and winding configuration, etc.), and if the casing is uniform along its length, then ki=kk and so:Bik=Gikki2  (5)orki={Bik/Gik}1/2  (6)Then Bij=GijKfij{Bik/Gik}1/2 and this is easily solved for the desired formation response Kfij.
That method has been used in field tests, but some problems remain. For example, variations in casing properties may occur on a scale small compared to the spacing of the transmitter and auxiliary receiver, it may be impractical to make the auxiliary coil identical to the transmitter coil, or the transmitter may operate in a non-linear manner.
Another method combining multiple auxiliary receivers-transmitters with the ratio idea has been tried. This method uses an auxiliary transmitter and receiver as shown in FIG. 3. In this case, the receiver Rj can also be used as a transmitter Tj and its signal detected by the receiver Rk. So the field at Rj from the main transmitter Ti is given by:Bij=Gijkikj  (7)and the field Bik at receiver Rk, is given by:Bik=Gikkikk  (8)Finally, the field Bjk at Rk due to transmitter Tj is given by:Bjk=Gjkkikk  (9)Since all the Bs and Gs are known, there are three equations in three unknowns: and ki, kj and kk. One can solve for ki since the field at the distant site, now denoted with subscript A, is given by:BiA=GiAKfiAki  (10)and with ki known, one can determine the desired KfiA.
The latter multiple auxiliary system is straight-forward in concept, but is complicated to implement in a practical system because the tool actually lowered into the hole is long and heavy. It does, however, have the advantage that nonlinear effects at the transmitter are included in the casing attenuation factor ki.
A related method uses what is known as the Remote-Field Eddy-Current (RFEC) principle to determine the inner diameter and/or the ratio of magnetic permeability to electric conductivity of a pipe. The method measures the mutual impedance of two induction coils (air-cored) separated by some distance and placed inside the pipe. That is one basis for non-destructively inspecting the conductive pipe that is widely used in the oilfield industry. The method, however, only permits an assessment of the inside of the pipe, and the results are highly sensitive to the variations in the magnetic permeability of the pipe, which can be significant. The method in general cannot be used to derive the EM signal attenuation through the pipe because of limitations on the parameters it can measure.
A method has been developed for use with non-magnetic casing by which measurement of the impedance of a transmitting (or receiving) solenoid at some frequency can be used to predict the attenuation of the field by the surrounding casing, as seen at a distant receiver (or from a distant transmitter). The method permits use of any frequency, irrespective of the conductivity of the casing or the thickness of the casing wall for casing having a given inner/outer diameter. The method is also applicable irrespective of the formation conductivity.
In addition, a method to predict the casing attenuation that is invariant with small changes in casing inner diameter was developed. One important finding is that both casing attenuation and impedance are simple functions of the product of the electric conductivity, thickness of the casing, and the operating EM frequency, which allows one to derive the casing attenuation factor directly from the impedance measurements.